Can exogenous variables be state features in reinforcement learning?
Including exogenous variables in your state representation certainly can be useful, as long as you expect them to be relevant information for determining the action to pick. So, state features are not only useful if you expect your agent (through application of actions) to have (partial) influence on those state variables; you just want the state variables themselves to be informative for your next action to take / prediction of expected future rewards.

However, if you only have exogenous variables, i.e. if you expect your agent to have no influence whatsoever on what states you'll end up in next... then the full problem definition typically used in RL (Markov decision processes) may be unnecessarily complex, and you may prefer to look into the Multi-Armed Bandits (MAB) problem formulation. If you're already familiar with RL / MDPs, you may think of MAB problems as (sequences of) single-step episodes, where you always just look at the current state and don't care at all about future states (because you expect to have 0 influence on them).

In theory, the RL / MDP framework is more general and is also applicable to those MAB problems, but RL algorithms that support this framework may perform worse than MAB algorithms in practice, because they (informally speaking) still put in effort trying to "learn" how their actions affect future states (a waste of effort when you expect there to be no such influence from the agent).